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Reference Crust-Mantle Density Contrast Beneath Antarctica Based on the Vening Meinesz-Moritz Isostatic Inverse Problem and CRUST2.0 Seismic Model

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Reference Crust-Mantle Density Contrast Beneath Antarctica Based on the Vening Meinesz-Moritz Isostatic Inverse Problem and CRUST2.0 Seismic Model EARTH SCIENCES RESEARCH JOURNAL Earth Sci. Res. SJ. Vol. 17, No. 1 (June, 2013): 7 -12 GEOPHYSICS Reference crust-mantle density contrast beneath Antarctica based on the Vening Meinesz-Moritz isostatic inverse problem and CRUST2.0 seismic model Robert Tenzer1 and Mohammad Bagherbandi2,3 1 Institute of Geodesy and Geophysics, School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan, China 2 Division of Geodesy and Geoinformatics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden 3 Department of Industrial Development, IT and Land Management University of Gävle, SE-80176 Gävle, Sweden ABSTRACT Key words: Antarctica, crust, gravity, isostasy, mantle, Moho interface. The crust-mantle (Moho) density contrast beneath Antarctica was estimated based on solving the Vening Meinesz-Moritz isostatic problem and using constraining information from a seismic global crustal model (CRUST2.0). The solution was found by applying a least-squares adjustment by elements method. Global geopotential model (GOCO02S), global topographic/bathymetric model (DTM2006.0), ice-thickness data for Antarctica (assembled by the BEDMAP project) and global crustal model (CRUST2.0) were used for computing isostatic gravity anomalies. Since CRUST2.0 data for crustal structures under Antarctica are not accurate (due to a lack of seismic data in this part of the world), Moho density contrast was determined relative to a reference homogenous crustal model having 2,670 kg/m3 constant density. Estimated values of Moho density contrast were between 160 and 682 kg/m3. The spatial distribution of Moho density contrast resembled major features of the Antarctic’s continental and surrounding oceanic tectonic plate configuration; maxima exceeding 500 kg/m3 were found throughout the central part of East Antarctica, with an extension beneath the Transantarctic mountain range. Moho density contrast in West Antarctica decreased to 400-500 kg/m3, except for local maxima up to ~ 550 kg/m3 in the central Antarctic Peninsula. RESUMEN Palabras clave: Antártida, corteza terrestre, manto terrestre, gravedad, isostasia, Discontinuidad de Mohorovičić El contraste de densidad de la discontinuidad de Mohorovičić (Moho) debajo de la Antártida fue estimado con base en la solución del problema isostático Vening Meinesz-Moritz y a partir de datos obtenidos con el modelo sísmico de la corteza global (CRUST2.0). La solución se encontró a través de un ajuste al método de mínimos cuadrados por el método de elementos. El modelo geopotencial global (GOCO02S), el modelo topográfico/ batimétrico (DTM2006.0), los datos de espesor del hielo para la Antártida (reunidos por el proyecto BEDMAP) y el modelo sísmico de corteza global (CRUST2.0) fueron utilizados para calcular las anomalías gravitatorias isostáticas. Ya que los datos de CRUST2.0 para las estructuras de la corteza en la Antártida no son exactos (debido a la falta de información sísmica para esta parte del planeta), el contraste de densidad de la Discontinuidad de Mohorovičić fue determinado a partir de un modelo de corteza homogéneo que tiene una densidad constante de 2,670 kg/m3. Los valores estimados del contraste de densidad de la Moho se encontraron entre 160 y 682kg/ m3. La distribución espacial del contraste de densidad de la Moho exhibe mayores rasgos en la configuración de la plancha tectónica de la Antártida continental y su alrededor oceánico. El valor máximo encontrado excede los Record 500 kg/m3 y se ubica en la parte Este continental, con extensión en las Montañas Transantárticas. El contraste de densidad de la Moho (zona de transición entre la corteza y el manto terrestre) en el Oeste de la Antártida osciló Manuscript received: 23/10/2012 entre 400-500 kg/m3, excepto para la máxima local de ~ 550 kg/m3, en el centro de la Península Antártida. Accepted for publication: 04/04/2013 Introduction based on localised controlled source seismic experiments. Passive seismic studies, based on earthquakes occurring mostly outside the Antarctic tec- Current knowledge about the lithospheric structure beneath An- tonic plate (due to a lack of intra-plate seismicity within the Antarctic tarctica is limited due to a low spatial coverage of high-quality seismic plate (Okal, 1981), still represent the primary source of information. data. Seismic studies by Kogan (1972) and Ito and Ikami (1986) were Studies based on an analysis of surface wave velocity can be found in Robert Tenzer and Mohammad Bagherbandi Evison et al., (1960), Kovach and Press (1961), Bentley and Ostenso the Bouguer gravity reduction term , which was defined by the (1962), Dewart and Toksoz (1965), Adams (1971), Knopoff and Vane coefficients of global topographic/bathymetric (density) spherical functions (1978), Rouland et al., (1985), Forsyth et al., (1987), Roult et al., (1994) . The coefficients were defined as (Sjöberg, 2009): and Bannister et al., (2003). Seismic receiver function analysis has been carried out by Reading (2006), Lawrence et al., (2006) and Winberry , (4) and Anandakrishnan (2004). Ritzwoller et al., (2001) used the simulta- neous inversion of broadband group velocity measurements to compile a seismic model of the crust and upper mantle beneath Antarctica and surrounding oceans. Some studies have been based on airborne gravi- where is the (fully-normalised) surface spherical harmonic function ty surveys, for instance by Studinger et al., (2004, 2006). Llubes et al., of degree n and order m . The density distribution function equals (2003) used CHAMP satellite gravity data for estimating crust thickness on land and ocean density contrast is defined as: ; where c is in Antarctica. More recently, Block et al., (2009) have estimated crust wareference crust density and mean saltwater density. Ice and sediment thickness in Antarctica using GRACE gravity data. density contrasts were defined relative to reference crust density c. Nominal ~ c Despite some authors having investigated Antarctic crust thickness, (zero-degree) compensation attraction g0 stipulated at the sphere of radius R studies addressing lithosphere density structure and density interface in was computed as from (Sjöberg, 2009): this part of the world are rare. This study was thus aimed at investigating Moho density contrast beneath Antarctic continental and surrounding oceanic crustal structures. Since large areas of Antarctica are not yet suffi- ciently covered by seismic surveys, current knowledge about crust density structure is not complete and accurate. A simple model of 2,670 kg/m3 , (5) homogenous crust reference density was thus adopted and Moho den- sity contrast was estimated regarding such crustal density. This involved where , and T0 and are the adopted nominal mean values applying the method recently developed by Sjöberg (2009) and Sjöberg of Moho depth and density contrast, respectively. and Bagherbandi (2011). Estimation principle Isostatic model Least-squares analysis was used for estimating T and ∆ρ . The lineari- The generic expression of solving the Vening Meinesz-Moritz isostatic pro- sed observation equation involved expanding the integral term on the left- blem was formulated in the following form (Sjöberg and Bagherbandi, 2011): hand side of equation (1) into a Taylor series. The subsequent substitution of the first two terms in the series for s n+3 from equation (3) to equation −GR∫∫ ∆ρ( Ω′′) K( ψ ,sd) Ω = ∆ g i ( r, Ω), (1) (1) yielded (Sjöberg and Bagherbandi, 2011): Φ where G = 6.674×10-11 m3 kg-1 s-2 is Newton’s gravitational constant, R = 6371×103 m Earth’s mean radius, ∆ρ Moho density contrast, ∆g i (approximate) isostatic gravity anomaly (cf. Sjöberg, 2009), K the integral . (6) kernel function, and dΩ′ = cosφ′dφ′dλ′ the infinitesimal surface element on the unit sphere. The 3-D position was defined in the spherical coordi- nates system (r,Ω), where r is the spherical radius and Ω = (φ,λ) denotes From equation (5), the linearised observation equation for product the spherical direction with spherical latitude φ and longitude λ . The full T ∆ρ was found in the following form: spatial angle is denoted as . Integral kernel K in equation (1) was defined for parametersψ and . (7) s, where ψ is the spherical distance between observation and (running) integration points (r,Ω) and (r′,Ω′), and s a ratio function of the Moho depth T and Earth’s mean radius R, i.e. s = 1−τ = 1−T / R. The spectral Approximation of term in equation (7) by yiel- representation of K was given by (Sjöberg, 2009): ded the linearised observation equation for ∆ρ in the following form: ∞ n +1 n+3 , (2) K(ψ , s) = ∑ (1− s ) Pn (cosψ ) . (8) n=0 n + 3 where Pn is the Legendre polynomial of degree n for the argument of Least-squares analysis combined the estimated product of T and ∆ρ cosine of the spherical distance ψ . with a priori values t and κ of such parameters for obtaining improved i The isostatic gravity anomaly ∆g computed at position (r,Ω) was estimates of T and ∆ρ. The system of observation equations was given in defined as follows (cf. Vening Meinesz, 1931): the following vector-matrix form: ∆g i (r,Ω) = ∆g B (r,Ω)+ g c (r,Ω) = 0, (3) , (9) where ∆g B is the refined Bouguer gravity anomaly, and g c the gravi- where is the vector of residuals. Parameter vector x and observation tational attraction of isostatic compensation masses (see also Bjerhammar, vector l read: 1962, Chap. 14, eqn. 5; Moritz, 1990). The spectral representation of isos- tatic gravity anomaly ∆g i was defined in terms of spherical harmonics , of degree n and order m. The numerical coefficients were generated (10) from spherical harmonic coefficients of gravity anomaly after applying Reference crust-mantle density contrast beneath Antarctica based on the Vening Meinesz-Moritz isostatic inverse problem and CRUST2.0 seismic model 2 Elements l1 , l2 and l3 of the observation vector l were formed, respecti- where unit weight variance σ 0 reads was: vely, by observables T ∆ρ, ∆ρ and T.
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